We introduce the notion of Γ continuity at a point x—where Γ is any pointclass—and give conditions under which Γ continuity at every x is equivalent to Γ measurability. Using this we extend the notion of the integral of a measurable function. Also we examine the case View the MathML sourceΓ=Σξ0, where View the MathML source(Σξ0)ξ<ω1 is the usual ramification of the class of Borel sets, see [A.S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, 1994].
A localization of Γ-measurability
GREGORIADES, VASSILIOS;
2008-01-01
Abstract
We introduce the notion of Γ continuity at a point x—where Γ is any pointclass—and give conditions under which Γ continuity at every x is equivalent to Γ measurability. Using this we extend the notion of the integral of a measurable function. Also we examine the case View the MathML sourceΓ=Σξ0, where View the MathML source(Σξ0)ξ<ω1 is the usual ramification of the class of Borel sets, see [A.S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, 1994].
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